Micro-electromechanical (MEM) Coriolis vibratory gyroscopes (CVG) have a mobile mechanical structure that is excited to perform a periodic oscillation. This periodic oscillation generated through excitation is also called primary oscillation. If the sensor undergoes a rotation around an axis perpendicular to the primary oscillation or primary movement, the movement of the primary oscillation will lead to a Coriolis force that is proportional to the measurement quantity, i.e. the angular velocity. This axis is called sensitive axis of the sensor. A second oscillation that is orthogonal to the primary oscillation is triggered by the Coriolis force. This second oscillation that is orthogonal to the primary oscillation is also called secondary oscillation or secondary movement. The secondary oscillation, which is also referred to as detection oscillation, can be detected by means of different measurement methods, wherein the detected quantity is used as a measure for the angular rate that impacts on the angular rate sensor. To create the primary oscillation, thermal, piezoelectric, electrostatic and inductive methods that are known in technology are used inter alia. To detect the secondary oscillation, piezoelectric, piezoresistive or capacitive principles are state of the art.
Angular rate sensors can be implemented in different ways. However, a common aspect of all angular rate sensors is that they comprise an oscillation device through which a primary excitation device can be set to perform the primary movement and that they have a secondary recording device that can measure a secondary movement due to an angular rate that impacts on the angular rate sensor. In case of non-decoupled sensors, the same oscillating mass performs both the primary movement as well as the secondary movement. This oscillation device is then formed in a way that it comprises a mass that is suspended flexibly in both the x-direction as well as in the y-direction. Without restricting the generality, it is assumed that the x-direction is the direction of the primary movement or of the primary oscillation, and that the y-direction is the direction of the secondary movement and/or of the secondary oscillation and that the angular rate impacts on the oscillation device in the z-direction.
The oscillation device is usually divided into a primary oscillator and a secondary oscillator. The primary oscillator performs an oscillation in the primary direction and is coupled with the secondary oscillator in a way that the primary oscillation is transferred to the secondary oscillator. The primary oscillator is ideally suspended on a substrate in a way that it can only move in the primary direction but not in the secondary direction. Hence and due to an angular rate, a Coriolis force that impacts on the primary oscillator does not lead to the primary oscillator being deflected in the secondary direction as this degree of movement space does not exist for the primary oscillator due to its suspension. On the other hand, the secondary oscillator is suspended in a way that it can move both in the primary direction as well as in the secondary direction. The secondary movement leads to a movement of the secondary oscillator in the secondary direction, wherein this secondary movement can be detected by the secondary detection device. Preferably, the secondary detection device is thereby formed in a way that it does not record the primary movement that the secondary oscillator performs only for the purpose of being sensitive to the Coriolis force. Moreover and to achieve an even better coupling, the connection between the primary oscillator and the secondary oscillator is formed in a way that, although the primary oscillation is transferred from the primary oscillator to the secondary oscillator, the secondary oscillation will not be transferred back onto the primary oscillator.
Angular rate sensors detect angular rates by a defined sensitive axis based on the Coriolis effect. As explained above, the angular rate sensor consists of two masses, i.e. the primary as well as the secondary mass. To be able to detect an angular rate by means of the Coriolis effect, the entire mass has to be set in motion. The primary mass, in which the secondary mass is suspended, is set to a constant oscillation, for example through electrostatic actuation with its resonance frequency. Through a rotation of the sensor around the sensitive axis, the Coriolis force Fc impacts on the secondary mass orthogonally to the primary axis according to the following equation (1) so that the secondary mass will be deflected.{right arrow over (F)}c=−2m{right arrow over (Ω)}×{right arrow over (v)}p  (1)
Here, m is the mass, Ω the angular rate and vp the velocity of the primary mass. The secondary mass is ideally mechanically suspended in a way that it can only deflect orthogonally to the primary oscillation. A large amplitude of the primary oscillation is desirable to achieve a high sensitivity. The primary mass is hereby usually excited resonantly and the amplitude of the oscillation is regulated by means of an automatic gain control (AGC) as known from the article T. Northemann, M. Maurer, S. Rombach, A. Buhmann, Y. Manoli: “Drive and sense interface for gyroscopes based on bandpass sigma-delta modulators”, Proc. IEEE Int. Circuits and Systems (ISCAS) Symp, pages 3264-3267, 2010.
FIG. 1 schematically displays an angular rate sensor with a primary control loop for the drive and a secondary control loop for reading out the signal. To achieve a high linearity, large bandwidths and a reduced sensitivity with regard to process fluctuations, the sensors as shown in FIG. 1 are operated with feedback on both the primary as well as on the secondary side. According to the following equation (2), the impacting Coriolis force {right arrow over (F)}C is compensated in the secondary control loop through the application of a resetting capacitive force:{right arrow over (F)}C={right arrow over (F)}es  (2)
Therefore, the secondary mass remains in the resting position and the generated force {right arrow over (F)}es forms a direct measure for the angular rate that acts upon the system.
The required compensation signal is usually generated through embedding of the sensor into a closed control loop of a delta-sigma modulator (in the following also abbreviated as ΔΣM). FIG. 2 schematically displays a simplified block diagram of a secondary control loop for operating an angular rate sensor based on the delta-sigma modulation. This way, the output signal is digitalized directly with a high resolution and a high linearity is achieved.
ΔΣM are based inter alia on noise shaping. In this process, quantization noise nq that is formed at the output is suppressed through filters, which are provided within the modulator, in the signal band and shifted towards other frequencies. During realization of an electromagnetic ΔΣM, also an additional electronic filter for noise shaping is used frequently besides the actual mechanical sensor element Hs(s). This filter Hf(s) is typically formed as a band pass filter. The noise transfer function (NTF) according to the following equation (3) and the signal transfer function (STF) according to equation (4) can be derived on this basis.
                    NTF        =                              Y                          n              q                                =                      1                          1              +                                                F                  ⁡                                      (                    s                    )                                                  ⁢                                  k                  q                                ⁢                                                      H                    s                                    ⁡                                      (                    s                    )                                                  ⁢                                                      H                    f                                    ⁡                                      (                    s                    )                                                                                                          (        3        )                                STF        =                              Y                          F              C                                =                                                                      k                  q                                ⁢                                                      H                    s                                    ⁡                                      (                    s                    )                                                  ⁢                                                      H                    f                                    ⁡                                      (                    s                    )                                                                              1                +                                                      F                    ⁡                                          (                      s                      )                                                        ⁢                                      k                    q                                    ⁢                                                            H                      s                                        ⁡                                          (                      s                      )                                                        ⁢                                                            H                      f                                        ⁡                                          (                      s                      )                                                                                            ≈                          1                              F                ⁡                                  (                  s                  )                                                                                        (        4        )            
Here, Y denominates the output signal of the as ΔΣM, kq a quantization constant, F(s) the transfer function of the feedback, Hf(s) the transfer function of the electric filter, Hs(s) the transfer function of the secondary mass.
To achieve the best possible signal-to-noise ratio (SNR), the resonance frequency ff of the electric filter Hf(s) has to be exactly in line with the primary resonance frequency of the angular rate sensor fd at which the angular rate signal is modulated. The typical power spectrum of the output Y of a ΔΣM is displayed in FIG. 3 for the case that the frequencies fd and ff do not match.
In particular in case of time-continuous filters Hf(s), which can be implemented very energy-efficiently, strong variations of the filter resonance frequency ff result during production and under the influence of temperature changes. In addition, the primary resonance frequency fd of angular rate sensors can also vary strongly through process variations. These fluctuations lead to the sensor readout circuits having to be set initially on one hand and to fluctuations having to be neutralized during operation on the other hand.
To avoid a reduction of the SNR, the setting of the frequency ff has to be very accurate. This means that the error between the filter and the sensor resonance frequency should be lower than the bandwidth (BW) of the angular rate signal. For example, a high required relative accuracy of 0.5% results from typical values for the bandwidth BW=50 Hz and sensor resonance frequencies fd=10 kHz.
Different concepts for setting a filter in a ΔΣM during operation are already known in the state of the art. The following examples thereby relate to both a purely electric ΔΣM for analog-to-digital conversion for which the problematic is very similar as well as to electromechanical ΔΣM for angular rate sensors.
For example the publication Tsividis, Y., “Integrated continuous-time filter design—an overview,” Solid-State Circuits, IEEE Journal of, vol. 29, no. 3, pp. 166, 176, March 1994, discloses the so-called master-slave principle in which two filters that are aligned to one another as well as possible are used. The basic structure for readjustment the filter frequency with the master-slave principle is shown in FIG. 4.
A filter Hfs(s) (slave) thereby works within the readout circuit whereas the other filter Hfm(s) (master) can be set outside by means of the primary resonance frequency and a phase-comparing device. Based on the assumption that both filters behave equally, the signal Vt can be used not only for the master filter but also for the slave filter.
This known method, however, cannot be used if the used electric filter has a considerable non-linearity. Especially time-continuous filters whose time constants are defined not by resistance or capacity conditions (RC) but by the transconductance of transistors and capacities (Gm-C) are a problem in this context. Gm-C filters are generally used because they can be implemented very energy-efficiently. However, they show a dependence of the transconductance gm (and consequently also of the resonance frequency) on the input voltage. The dependence shall be neglected for the operation within the secondary control circuit as, according to FIG. 2 and according to the following equation (5), the signal at the input of the filter Vfilt for the resonance frequency ff is suppressed by the overall control circuit with the gain of the filter Hf(s):
                              V          filt                =                                            F              C                        -                          n              q                                            1                                                            H                  s                                ⁡                                  (                  s                  )                                            +                                                H                  f                                ⁡                                  (                  s                  )                                                                                        (        5        )            
If however, as in case of the master-slave method, the actual frequency adjustment is performed outside of the readout loop, problems can arise. If a signal with the desired resonance frequency is applied directly to the input of such a filter, this will cause strong detuning of the filter frequency due to the high signal amplitudes in the filter and/or the high gain in case of resonance. Reliable setting will no longer be possible.
In addition, the accuracy of this known method is in particular limited to a frequently intolerable value by the restricted match of the two used filters. Furthermore, the surface requirement is relatively high for an implementation as an integrated circuit because a further analog filter is needed in addition to the circuit for the automated frequency adjustment.
Another known concept that is based on two separate filters but that requires no exact match of the filters is described in the article Afifi, M.; Maurer, M.; Hehn, T.; Taschwer, A.; Manoli, Y., “An automatic tuning technique for background frequency calibration in gyroscope interfaces based on high order bandpass Delta-Sigma modulators,” Circuits and Systems (ISCAS), 2015 IEEE International Symposium on, pp. 1730, 1733, 24-27 May 2015, for the use in a readout circuit for angular rate sensors. As shown in FIG. 5, one filter is used within the readout circuit while the other one is set outside by means of the primary resonance frequency also this concept. In contrast to the first method, both filters, however, are replaced periodically so that the readout circuit only has to be interrupted for a short moment. At the same time, it is assumed that the filter in the readout circuit is not subjected to any significant change of the resonance frequency during a period of the replacement circuit.
This principle of the periodically replaced filters is already described in the publication Tsividis, Y., “Self-tuned filters,” Electronics Letters, vol. 17, no. 12, pp. 406, 407, Jun. 111981, for the general application in time-continuous filters as well.
However, the same problems occur in this concept of the periodically replaced filters due to the non-linearity of the filters like in case of the master-slave concept. In addition, the filter has to be decoupled periodically and there is consequently the risk of impairment of the functionality of the secondary control circuit. Furthermore, the surface requirement in case of an implementation as an integrated circuit is relatively high also for this known arrangement as a further analog filter is needed in addition to the circuit for the automated frequency adjustment.
It is further known to examine the power of two spectral points at the output of the ΔΣM. In the publication Huanzhang Huang; Lee, E. K. F., “Frequency and Q tuning techniques for continuous-time bandpass sigma-delta modulator,” Circuits and Systems, 2002. ISCAS 2002. IEEE International Symposium on, vol. 5, no., pp. V-589, V-592 vol. 5, 2002, the principle of a circuit for frequency adjustment of the filter in purely electric ΔΣM is described. Two different approaches for determining the noise power at the output of the modulator at two different points fa and/or fb, which are located slightly above and/or below the actual signal frequency around fd, are presented. As the electric filter influences the noise power differently on these discreet frequencies as a function of the position of its resonance frequency, the absolute value of the two noise powers can be used to determine whether the filter resonance frequency is too high or too low. FIG. 6a illustrates the principle based on the spectrum of the output Y of the secondary control circuit of the ΔΣM when fd and ff are matching. Accordingly, FIG. 6b shows the case of ff being too high. The discreet signal components fa and fb in the spectrum of the output Y are compared in order to estimate the current filter frequency. According to a first approach of this known solution, a discreet Fourier transformation (DFT) is formed at the points fa and fb by means of digital signal processing. This concept is displayed schematically in FIG. 7a. 
According to a second approach of the publication Huanzhang Huang; Lee, E. K. F., “Frequency and Q tuning techniques for continuous-time bandpass sigma-delta modulator,” Circuits and Systems, 2002. ISCAS 2002. IEEE International Symposium on, vol. 5, pp. V-589, V-592 vol. 5, 2002, the frequencies to be examined, as sketched in FIG. 7b, are filtered out by means of two additional digital filters with a very narrow bandwidth. Subsequently, the power of both signals is calculated and compared. A digital control unit adjusts the filter respectively according to the comparative result.
This solution is disadvantageous in cases where the readout loop has more then only one filter. This is typically the case for electromagnetic ΔΣM for angular rate sensors as also the mechanical element is used for filtering according to equation (4) besides the electric filter. As a result, the NTF and consequently the noise is determined at the output of two independent filter elements. However, it is not possible to distinguish which one of the two filters has to be set.
In addition, only two discreet frequency components, which have to be outside of the signal band, are examined in this known method. Therefore, the accuracy of the control is limited and many measurements have to be averaged. Averaging of multiple measurements, however, leads in turn to a slower progression of the frequency adjustment. In particular for applications that are exposed to fast temperature fluctuations, this can be intolerable. Even more striking is the condition that, due to the limited frequency selectivity, a signal in the signal band leads to disruptions of the filter control loop.
Further, the publication Huanzhang Huang; Lee, E. K. F., “Frequency and Q tuning techniques for continuous-time bandpass sigma-delta modulator,” Circuits and Systems, 2002. ISCAS 2002. IEEE International Symposium on, vol. 5, pp. V-589, V-592 vol. 5, 2002, states that both implementation variants result in a similar space requirement. Taking the second variant as a basis, however, there is an equally high surface requirement with regard to the filter to be set due to two additional digital band pass filters, two multipliers and two integrators.
A further known solution is based on the input of test signals. As described in the publication Yun-Shiang Shu; Bang-Sup Song; Bacrania, K., “A 65 nm CMOS CT ΔΣ Modulator with 81 dB DR and 8 MHz BW Auto-Tuned by Pulse Injection,” Solid-State Circuits Conference, 2008. ISSCC 2008. Digest of Technical Papers. IEEE International, pp. 500, 631, 3-7 Feb. 2008, and illustrated in FIG. 8a for an electromagnetic ΔΣM, a test signal Vtest with exactly one frequency is input into the control loop after the filter with a purely electric ΔΣM in this solution. Then, it is verified how the test signal is suppressed by the filter transfer function at the digital output Y of the modulator. Depending on the phase situation and size of the remaining test signal at the output Y, conclusions can be drawn about whether the filter resonance frequency ff is too high or too low. A digital control unit readjusts the filter accordingly. FIG. 8b shows such a known circuit for evaluating the input test signals.
The patent specification U.S. Pat. No. 7,042,375 B2 further describes a principle in which a broadband spectrum (dither) is used as a test signal Vtest instead of exactly one frequency. Evaluation of the signal at the output Y is done in a similar way as illustrated in FIGS. 7b or 8b. 
The publication U.S. Pat. No. 7,324,028 B2 describes the input of test signals before or after the quantizer and in addition the bridging of individual filter elements.
Further, it is known from Ezekwe, C. D.; Boser, B. E., “A Mode-Matching ΔΣ Closed-Loop Vibratory-Gyroscope Readout Interface with a 0.004°/s/√Hz Noise Floor over a 50 Hz Band,” in Solid-State Circuits Conference, 2008. ISSCC 2008. Digest of Technical Papers. IEEE International, vol., no., pp. 580-637, 3-7 Feb. 2008, that the test signals shall not be input in the readout loop in the way that is shown in FIG. 8a after the filter element, but ahead of the filter element Hf(s). This way, not the electric filter Hf(s) but the resonance frequency of the secondary mass Hs(s) can be set. The particularity in this known implementation and the underlying concept from the publication DE 19910 415 A1 is that the test signals are situated differentially around the actual resonance frequency and not within the signal band. But the fundamental approach is possible for the setting of the electric filter Hf(s) as well.
Also this solution is disadvantageous when the readout loop contains more than only one filter. As mentioned, this is typically the case in electromagnetic ΔΣM for angular rate sensors as also the mechanical element for filtering according to equation (4) is used besides the electric filter. As a consequence, the NTF and hence the noise at the output of two independent filter elements is determined. However, it is not possible to distinguish which one of the two filters has to be set.
A considerable disadvantage of a part of the methods using test signals is that the test signal is situated directly in the signal band and that it is never suppressed perfectly due to the limited resolution. Therefore, the remaining test signal can disrupt the operation of the actual readout loop. Furthermore, the time until the secondary control loop can be used after the start is increased in case of this method. This is because, in contrast to the other explained methods, an incorrectly set filter does not only mean in these variants that the SNR is worse but also that the test signal is not suppressed. It can therefore not be distinguished from a possible angular rate signal. In the known implementation according to Ezekwe, C. D.; Boser, B. E., “A Mode-Matching ΔΣ Closed-Loop Vibratory-Gyroscope Readout Interface with a 0.004°/s/√Hz Noise Floor over a 50 Hz Band,” in Solid-State Circuits Conference, 2008. ISSCC 2008. Digest of Technical Papers. IEEE International, vol., no., pp. 580-637, 3-7 Feb. 2008, and DE 19910415 A1, the signals should be outside of the bandwidth of the angular rate signal. This results in a compromise between a maximum bandwidth and control accuracy.
In addition and depending on the implementation, there is a significant additional surface requirement for the generation of the test signals and the input into the readout loop besides the surface requirement for the evaluation of the test signals so that a disadvantageously high surface requirement shall be assumed for an implementation as an integrated circuit.
None of the solutions known so far consequently fulfills all requirements for an automated frequency adjustment of electric filters during operation in closed control loops with regard to applicability, functionality, and surface requirement of an implementation as an integrated circuit.